Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be the most (...) useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

An impressive review of brain neurophysiology provides the basis for modelling the dynamics of transmission in neural circuits, using appropriate nonlinear mathematics. The coverage is unbalanced, however: the parallel dynamics at the level of behaviour and sensory-cognitive processes are sparsely addressed, so the final chapter fails to indicate the complexity and subtlety of relevant modern work.

Alternative models of similarity judgments that do not rest on metric space assumptions are known to be better descriptions of actual human behaviour but are ignored by Edelman. The internal spaces he postulates are a convenient fiction for artificial intelligence, but not compatible with what is now known about psychophysics at both behavioural and neurological levels of perceptual processing.

Although one can endorse the complexity of the data and processes that Phillips & Singer (P&S) review, their mathematical suggestions can be compared critically with cases in nonlinear psychophysics, where the theoretician is faced with analogous problems. Owing to P&S's failure adequately to recognise both the intricate properties of nonlinear dynamics in networks and the constraints of metabolic demands on the temporal generation of patterns in biological nets their conclusions fail to meet the problems they properly address.

Chow's account of Bayesian inference logic and procedures is replete with fundamental misconceptions, derived from secondary sources and not adequately informed by modern work. The status of subjective probabilities in Bayesian analyses is misrepresented and the cogent reasons for the rejection by many statisticians of the curious inferential hybrid used in psychological research are not presented.